class_docstr: Isolation Forest Algorithm
  
  Return the anomaly score of each sample using the IsolationForest algorithm
  
  The IsolationForest 'isolates' observations by randomly selecting a feature
  and then randomly selecting a split value between the maximum and minimum
  values of the selected feature.
  
  Since recursive partitioning can be represented by a tree structure, the
  number of splittings required to isolate a sample is equivalent to the path
  length from the root node to the terminating node.
  
  This path length, averaged over a forest of such random trees, is a
  measure of normality and our decision function.
  
  Random partitioning produces noticeably shorter paths for anomalies.
  Hence, when a forest of random trees collectively produce shorter path
  lengths for particular samples, they are highly likely to be anomalies.
  
  Read more in the :ref:`User Guide <isolation_forest>`.
  
  .. versionadded:: 0.18
  
  Parameters
  ----------
  n_estimators : int, optional (default=100)
      The number of base estimators in the ensemble.
  
  max_samples : int or float, optional (default="auto")
      The number of samples to draw from X to train each base estimator.
          - If int, then draw `max_samples` samples.
          - If float, then draw `max_samples * X.shape[0]` samples.
          - If "auto", then `max_samples=min(256, n_samples)`.
      If max_samples is larger than the number of samples provided,
      all samples will be used for all trees (no sampling).
  
  contamination : float in (0., 0.5), optional (default=0.1)
      The amount of contamination of the data set, i.e. the proportion
      of outliers in the data set. Used when fitting to define the threshold
      on the decision function.
  
  max_features : int or float, optional (default=1.0)
      The number of features to draw from X to train each base estimator.
  
          - If int, then draw `max_features` features.
          - If float, then draw `max_features * X.shape[1]` features.
  
  bootstrap : boolean, optional (default=False)
      If True, individual trees are fit on random subsets of the training
      data sampled with replacement. If False, sampling without replacement
      is performed.
  
  n_jobs : integer, optional (default=1)
      The number of jobs to run in parallel for both `fit` and `predict`.
      If -1, then the number of jobs is set to the number of cores.
  
  random_state : int, RandomState instance or None, optional (default=None)
      If int, random_state is the seed used by the random number generator;
      If RandomState instance, random_state is the random number generator;
      If None, the random number generator is the RandomState instance used
      by `np.random`.
  
  verbose : int, optional (default=0)
      Controls the verbosity of the tree building process.
  
  
  Attributes
  ----------
  estimators_ : list of DecisionTreeClassifier
      The collection of fitted sub-estimators.
  
  estimators_samples_ : list of arrays
      The subset of drawn samples (i.e., the in-bag samples) for each base
      estimator.
  
  max_samples_ : integer
      The actual number of samples
  
  References
  ----------
  .. [1] Liu, Fei Tony, Ting, Kai Ming and Zhou, Zhi-Hua. "Isolation forest."
         Data Mining, 2008. ICDM'08. Eighth IEEE International Conference on.
  .. [2] Liu, Fei Tony, Ting, Kai Ming and Zhou, Zhi-Hua. "Isolation-based
         anomaly detection." ACM Transactions on Knowledge Discovery from
         Data (TKDD) 6.1 (2012): 3.
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docstr: Average anomaly score of X of the base classifiers.
  
  The anomaly score of an input sample is computed as
  the mean anomaly score of the trees in the forest.
  
  The measure of normality of an observation given a tree is the depth
  of the leaf containing this observation, which is equivalent to
  the number of splittings required to isolate this point. In case of
  several observations n_left in the leaf, the average path length of
  a n_left samples isolation tree is added.
  
  Parameters
  ----------
  X : {array-like, sparse matrix}, shape (n_samples, n_features)
      The training input samples. Sparse matrices are accepted only if
      they are supported by the base estimator.
  
  Returns
  -------
  scores : array of shape (n_samples,)
      The anomaly score of the input samples.
      The lower, the more abnormal.
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code: def decision_function(self, X):
      """Average anomaly score of X of the base classifiers.
  
      The anomaly score of an input sample is computed as
      the mean anomaly score of the trees in the forest.
  
      The measure of normality of an observation given a tree is the depth
      of the leaf containing this observation, which is equivalent to
      the number of splittings required to isolate this point. In case of
      several observations n_left in the leaf, the average path length of
      a n_left samples isolation tree is added.
  
      Parameters
      ----------
      X : {array-like, sparse matrix}, shape (n_samples, n_features)
          The training input samples. Sparse matrices are accepted only if
          they are supported by the base estimator.
  
      Returns
      -------
      scores : array of shape (n_samples,)
          The anomaly score of the input samples.
          The lower, the more abnormal.
  
      """
      # code structure from ForestClassifier/predict_proba
      # Check data
      X = self.estimators_[0]._validate_X_predict(X, check_input=True)
      n_samples = X.shape[0]
  
      n_samples_leaf = np.zeros(
          (n_samples, self.n_estimators), order="f"
      )
      depths = np.zeros((n_samples, self.n_estimators), order="f")
  
      for i, tree in enumerate(self.estimators_):
          leaves_index = tree.apply(X)
          node_indicator = tree.decision_path(X)
          n_samples_leaf[:, i] = tree.tree_.n_node_samples[leaves_index]
          depths[:, i] = (
              np.asarray(node_indicator.sum(axis=1)).reshape(-1) - 1
          )
  
      depths += _average_path_length(n_samples_leaf)
  
      scores = 2 ** (
          -depths.mean(axis=1) / _average_path_length(self.max_samples_)
      )
  
      # Take the opposite of the scores as bigger is better (here less
      # abnormal) and add 0.5 (this value plays a special role as described
      # in the original paper) to give a sense to scores = 0:
      return 0.5 - scores
  
file_path: catboost/contrib/python/scikit-learn/py2/sklearn/ensemble/iforest.py
imports: from __future__ import division
  import numpy
  import scipy
  from warnings import warn
  from scipy.sparse import issparse
  import numbers
  from ..externals import six
  from ..tree import ExtraTreeRegressor
  from ..utils import check_random_state, check_array
  from .bagging import BaseBagging
label_desc: Use image node_id 5 for calling the IsolationForest obj's underlying member method code with example usage: obj.decision_function(X) and returns: unknown